Maths-
General
Easy

Question

If the angles of triangle are in the ratio 1:1:4 then ratio of the perimeter of triangle to its largest side

  1. square root of 3 plus 2 colon square root of 2
  2. square root of 3 plus 2 colon square root of 3
  3. square root of 2 plus 2 colon square root of 3
  4. 3:2

hintHint:

The law of sines says that the ratio of the sine of one angle to the opposite side is the same ratio for all three angleslaw of sines.

The correct answer is: square root of 2 plus 2 colon square root of 3


    T h e space a n g l e s space o f space t h e space t r i a n g l e space A B C space a r e space d e n o t e d space b y space A comma space B comma space C space a n d space t h e space c o r r e s p o n d i n g space o p p o s i t e space s i d e s space b y space a comma space b comma space c.
s o space W e space k n o w space t h a t comma space
fraction numerator a over denominator sin space A end fraction space equals space fraction numerator b over denominator sin space B end fraction space equals space fraction numerator c over denominator sin space C end fraction space equals 2 R

    If the angles of triangle are in the ratio 1:1:4 .

    sin A space colon space sin B space colon space sin C space equals space 1 space colon space 1 space colon space 4
space fraction numerator a over denominator 2 R end fraction space colon space fraction numerator b over denominator 2 R end fraction space colon space fraction numerator c over denominator 2 R end fraction space equals space 1 space colon space 1 space colon space 4 space
space left curly bracket space fraction numerator a over denominator 2 R end fraction equals 1 semicolon space fraction numerator b over denominator 2 R end fraction equals 1 space colon fraction numerator c over denominator 2 R end fraction equals 4 space right curly bracket
space space a equals 2 R semicolon space b equals 2 R semicolon space c equals 8 R space
    If a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c
    According to question,
    Ratio of the perimeter of triangle to its largest side.. fraction numerator a space plus space b space plus space c space over denominator c end fraction space space space space left curly bracket space b c z space o f space a n g l e space C space i s space g r e a t e s t comma space c space s i d e space i s space g r e a t e r space t h a n space o t h r e s space right curly bracket
fraction numerator 2 R space plus space 2 R space plus space 8 R space over denominator 8 R end fraction space equals space fraction numerator 12 R over denominator 8 R end fraction space equals 3 over 2

    if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c .

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